FLEXI: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization variants, discontinuous Galerkin schemes offer a collection of advantageous features which have lead to a strong increase in interest in them and related formulations in the last decade. The methods have matured sufficiently to be of practical use for a range of problems, for example in direct numerical and large eddy simulation of turbulence. However, in order to take full advantage of the potential benefits of these methods, all steps in the simulation chain must be designed and executed with HO in mind. Especially in this area, many commercially available closed-source solutions fall short. In this work, we therefore present the extit{FLEXI} framework, a HO consistent, open-source simulation tool chain for solving the compressible Navier-Stokes equations on CPU clusters. We describe the numerical algorithms and implementation details and give an overview of the features and capabilities of all parts of the framework. Beyond these technical details, we also discuss the important but often overlooked issues of code stability, reproducibility and user-friendliness. The benefits gained by developing an open-source framework are discussed, with a particular focus on usability for the open-source community. We close with sample applications that demonstrate the wide range of use cases and the expandability of extit{FLEXI} and an overview of current and future developments.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Kurz, Marius; Beck, Andrea: A machine learning framework for LES closure terms (2022)
  2. Mossier, Pascal; Beck, Andrea; Munz, Claus-Dieter: A p-adaptive discontinuous Galerkin method with hp-shock capturing (2022)
  3. Zeifang, Jonas; Schütz, Jochen: Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method (2022)
  4. Bragin, M. D.; Kriksin, Yu. A.; Tishkin, V. F.: Entropic regularization of the discontinuous Galerkin method in conservative variables for two-dimensional Euler equations (2021)
  5. Dürrwächter, Jakob; Kurz, Marius; Kopper, Patrick; Kempf, Daniel; Munz, Claus-Dieter; Beck, Andrea: An efficient sliding mesh interface method for high-order discontinuous Galerkin schemes (2021)
  6. Dürrwächter, Jakob; Meyer, Fabian; Kuhn, Thomas; Beck, Andrea; Munz, Claus-Dieter; Rohde, Christian: A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations (2021)
  7. Krais, Nico; Beck, Andrea; Bolemann, Thomas; Frank, Hannes; Flad, David; Gassner, Gregor; Hindenlang, Florian; Hoffmann, Malte; Kuhn, Thomas; Sonntag, Matthias; Munz, Claus-Dieter: FLEXI: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws (2021)
  8. Laughton, Edward; Tabor, Gavin; Moxey, David: A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods (2021)
  9. Michael Schlottke-Lakemper; Gregor Gassner; Hendrik Ranocha; Andrew Winters; et al.: Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing (2021) arXiv
  10. Rueda-Ramírez, Andrés M.; Hennemann, Sebastian; Hindenlang, Florian J.; Winters, Andrew R.; Gassner, Gregor J.: An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. II: Subcell finite volume shock capturing (2021)
  11. Schneider, Teseo; Panozzo, Daniele; Zhou, Xianlian: Isogeometric high order mesh generation (2021)
  12. Beck, Andrea D.; Zeifang, Jonas; Schwarz, Anna; Flad, David G.: A neural network based shock detection and localization approach for discontinuous Galerkin methods (2020)
  13. Krais, Nico; Schnücke, Gero; Bolemann, Thomas; Gassner, Gregor J.: Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows (2020)